Warm-up
Three quick questions from earlier lessons.
Discover
On a map, 1 cm stands for 5 km. Two towns are 4 cm apart on the map. How far apart are they?
- 20 km
- 0.8 km
Key idea
A scale links drawing lengths to real lengths.
A scale like “1 cm to 5 km” says what one unit on the drawing stands for. Drawing → real: multiply; real → drawing: divide. A scale without units, like 1 to 200, means real lengths are 200 times the drawing lengths in the same unit.
Worked example
Scale 1 to 50; a table is 3 cm long on the drawing.
cm
Same unit.
m
100 cm = 1 m.
Your turn, guided
Your turn: scale 1 inch to 4 feet. A 28-foot wall on the plan (inches).
28 ÷ 4.
Practice ★
- On a map, 1 cm represents 9 km. Two towns are 6 cm apart on the map. How far apart are they in reality (km)?
- On a map, 1 cm represents 16 km. Two towns are 6 cm apart on the map. How far apart are they in reality (km)?
- A floor plan uses the scale 1 inch to 4 feet. A wall is 20 feet long. How long is it on the plan (inches)?
Watch out!
Practice ★★
- A drawing has a scale of 1 to 450 (no units). A line on it is 11 cm long. How long is the real object in meters?
- A drawing has a scale of 1 to 400 (no units). A line on it is 8 cm long. How long is the real object in meters?
Exit ticket
Three questions to check you have got it.
- On a map, 1 cm represents 9 km. Two towns are 6 cm apart on the map. How far apart are they in reality (km)?
- On a map, 1 cm represents 16 km. Two towns are 6 cm apart on the map. How far apart are they in reality (km)?
- On a map, 1 cm represents 5 km. Two towns are 14 cm apart on the map. How far apart are they in reality (km)?
Summary card
Scale drawings
Drawing → real: multiply by the scale; real → drawing: divide.
Watch out: convert units at the end.
End of the lesson
Next lesson: Scaled copies: lengths and areas Back to the chapter